- #1
osturk
- 11
- 0
Hello everyone,
I'm trying to calculate the doppler shift in frequency of a moving source. I'm approaching the problem from two different frames of reference and getting inconsistent results. what am I missing here?
consider the special case of transverse doppler effect (θ=π/2). light reaches observer from y-direction.
reference frame 1: source traveling towards x-direction. observer at rest.
Δto=1/fo - observer's time between subsequent wave crests.
due to time dilation, source's time should be running slower Δ[itex]\tau[/itex]s=Δto/[itex]\gamma[/itex], so actual frequency of source is 1/Δ[itex]\tau[/itex]s=fs=fo*[itex]\gamma[/itex] (the correct relation)
reference frame 2: observer traveling towards x-direction. source at rest.
Δts=1/fs - source's time between subsequent wave crests.
due to time dilation, observer's time should be running slower Δ[itex]\tau[/itex]o=Δts/[itex]\gamma[/itex], so frequency observed is 1/Δ[itex]\tau[/itex]o=fo=[itex]\gamma[/itex]fs
which leaves actual frequenct of source fs=fo/[itex]\gamma[/itex]
why are these two results seemingly inconsistent?
thanks in advance.
I'm trying to calculate the doppler shift in frequency of a moving source. I'm approaching the problem from two different frames of reference and getting inconsistent results. what am I missing here?
consider the special case of transverse doppler effect (θ=π/2). light reaches observer from y-direction.
reference frame 1: source traveling towards x-direction. observer at rest.
Δto=1/fo - observer's time between subsequent wave crests.
due to time dilation, source's time should be running slower Δ[itex]\tau[/itex]s=Δto/[itex]\gamma[/itex], so actual frequency of source is 1/Δ[itex]\tau[/itex]s=fs=fo*[itex]\gamma[/itex] (the correct relation)
reference frame 2: observer traveling towards x-direction. source at rest.
Δts=1/fs - source's time between subsequent wave crests.
due to time dilation, observer's time should be running slower Δ[itex]\tau[/itex]o=Δts/[itex]\gamma[/itex], so frequency observed is 1/Δ[itex]\tau[/itex]o=fo=[itex]\gamma[/itex]fs
which leaves actual frequenct of source fs=fo/[itex]\gamma[/itex]
why are these two results seemingly inconsistent?
thanks in advance.